It's unclear but...
Looking at the definitions provided for Wisdom and Charisma on the abilities page, there is not a clear definition of saving throws listed for the abilities.
Wisdom
Wisdom reflects how attuned you are to the world around you and represents perceptiveness and intuition.
Charisma
Charisma measures your ability to interact effectively with others. It includes such factors as confidence and eloquence, and it can represent a charming or commanding personality.
Like you, I have also heard and read of Charisma as a sort of 'force of personality', though I'm having trouble finding that in a source book. In any case, I think what we need to turn to is the spell lists that require each type of throw.
For PHB Spells that require wisdom saving throws, we see things like: Charm Person, Command, Compulsion, Dominate Person, Enthrall, Hideous Laughter, and Polymorph.
For PHB Spells that require charisma saving throws, we see things like: Banishment, Calm Emotions, Planar Binding and Seeming.
Clearly there is some overlap, but I think we can draw some rough boundaries.
When making a Wisdom saving throw, you are retaining your attunement to reality by resisting magical effects that attempt to trick you into behaving differently thenthan you would normally, or take advantage of your unconscious. On a failure, your intuition has failed and you cannot correctly perceive the world as it truly is. An enemy is a friend or master instead. For the spell Scrying you are attuned enough to the forces of magic that you can detect an incoming spy and resist it.
When making a Charisma saving throw, you are using your force of personality to resist a physical alteration of the world. On a failure, your confidence is shattered so much that you are physically banished or restrained. You have lost your command of reality.
Ultimately though, you are correct. It is a fine line.